In this paper we describe an application of the theory of graph transformations to the practise of language design. In particular, we have defined the static and dynamic semantics of a small but realistic object-oriented language (called TAAL) by mapping the language constructs to graphs (the static semantics) and modelling their effect by graph transformation rules (the dynamic semantics). This gives rise to execution models for all TAAL-programs, which can be used as the basis for formal verification.This work constitutes a first step towards a method for defining all aspects of software languages, besides their concrete syntax, in a consistent and rigorous manner. Such a method facilitates the integration of formal correctness in the software development trajectory.